Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63044 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,18)(19,21)(23,28)(29,39)(30,40)(31,41)(42,50)(43,51)(44,45)(52,53);(15,18)(19,20)(23,28)(24,32)(30,40)(31,41)(33,46)(34,47)(44,45)(48,49);(14,15)(16,19)(17,18)(20,21)(22,23)(24,29)(25,30)(26,31)(27,28)(32,39)(33,42)(34,43)(35,44)(36,40)(37,45)(38,41)(46,50)(47,51)(48,52)(49,53);(14,16)(15,19)(17,21)(18,20)(22,24)(23,29)(25,33)(26,34)(27,32)(28,39)(30,42)(31,43)(35,48)(36,46)(37,49)(38,47)(40,50)(41,51)(44,52)(45,53);(22,25,27,36)(23,30,28,40)(24,33,32,46)(26,37,38,35)(29,42,39,50)(31,45,41,44)(34,49,47,48)(43,53,51,52);(22,26,27,38)(23,31,28,41)(24,34,32,47)(25,35,36,37)(29,43,39,51)(30,44,40,45)(33,48,46,49)(42,52,50,53)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56032);